Den torsdagen den 1:e augusti 2013 kl. 22:24:02 UTC+2 skrev Peter Percival: > firstname.lastname@example.org wrote: > > > > > > > > And i may claim that Pi is a rational, because i know i can write it as a continued fraction. > > > > Writeable as a continued fraction is not the definition of rational.
The convergents of a continued fraction expansion of x give the best rational approximations to x.
Continued fractions can be thought of as an alternative to digit sequences for representing numbers, based on division rather than multiplication by a base. Studied occasionally for at least half a millennium, continued fractions have become increasingly important through their applications to dynamical systems theory and number theoretic algorithms. Mathematica has highly efficient original algorithms for finding large numbers of terms in continued fractions, as well as for handling exact continued fractions for quadratic irrationals.
> > > > The real funny thing is that this was known to mathematicians 11 BC. So your not that sofisticated. > > > > He can probably spell though. > > > > -- > > Nam Nguyen in sci.logic in the thread 'Q on incompleteness proof' > > on 16/07/2013 at 02:16: "there can be such a group where informally > > it's impossible to know the truth value of the abelian expression > > Axy[x + y = y + x]".